The prices for rights of use are determined by market, but usually bundled together with prices of buildings on it.
One way to look at Georgist critique of current land system is that the rights of use are sold once but held infinitely long. If you got lucky and bought a piece of land in downtown Manhattan 200 years ago for 20 bucks, now you wouldn't need to pay anyone for granting you that ownership right. Basically land (and natural resources) are owned by people who got lucky, not by people who actually use it (such as a restaurant which has to rent it from that lucky holder). If the ownership rights were not given for infinite amount of time but reentered into an auction every, say 7 years, the allocation of land would then go to people who actually need it. It is the same economical problem as Domain Name allocation on web.
People 'own' land on paper only. The government actually owns it no matter if you are in China, Europe or United States.